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<div class="fragment"><pre class="fragment"><a name="l00001"></a>00001 <span class="comment">#!/usr/bin/python</span>
<a name="l00002"></a>00002 <span class="comment"># -*- coding: utf-8 -*-</span>
<a name="l00003"></a>00003 
<a name="l00004"></a>00004 <span class="comment"># Copyright (c) 2011</span>
<a name="l00005"></a>00005 <span class="comment">#</span>
<a name="l00006"></a>00006 <span class="comment"># Permission is hereby granted, free of charge, to any person obtaining a</span>
<a name="l00007"></a>00007 <span class="comment"># copy of this software and associated documentation files (the &quot;Software&quot;),</span>
<a name="l00008"></a>00008 <span class="comment"># to deal in the Software without restriction, including without limitation</span>
<a name="l00009"></a>00009 
<a name="l00010"></a>00010 <span class="comment"># the rights to use, copy, modify, merge, publish, distribute, sublicense,</span>
<a name="l00011"></a>00011 <span class="comment"># and/or sell copies of the Software, and to permit persons to whom the</span>
<a name="l00012"></a>00012 <span class="comment"># Software is furnished to do so, subject to the following conditions:</span>
<a name="l00013"></a>00013 <span class="comment">#</span>
<a name="l00014"></a>00014 <span class="comment"># The above copyright notice and this permission notice shall be included in</span>
<a name="l00015"></a>00015 <span class="comment"># all copies or substantial portions of the Software.</span>
<a name="l00016"></a>00016 <span class="comment">#</span>
<a name="l00017"></a>00017 <span class="comment"># THE SOFTWARE IS PROVIDED &quot;AS IS&quot;, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR</span>
<a name="l00018"></a>00018 <span class="comment"># IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,</span>
<a name="l00019"></a>00019 <span class="comment"># FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE</span>
<a name="l00020"></a>00020 <span class="comment"># AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER</span>
<a name="l00021"></a>00021 <span class="comment"># LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,</span>
<a name="l00022"></a>00022 <span class="comment"># OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE</span>
<a name="l00023"></a>00023 <span class="comment"># SOFTWARE.</span>
<a name="l00024"></a>00024 <span class="comment">#</span>
<a name="l00025"></a>00025 <span class="comment"># Author: Jesus Carrero &lt;j.o.carrero@gmail.com&gt;</span>
<a name="l00026"></a>00026 <span class="comment"># Mountain View, CA</span>
<a name="l00027"></a>00027 <span class="comment">#</span>
<a name="l00028"></a>00028 
<a name="l00029"></a>00029 <span class="keyword">from</span> scipy.linalg <span class="keyword">import</span> norm
<a name="l00030"></a>00030 <span class="keyword">from</span> scipy <span class="keyword">import</span> array
<a name="l00031"></a>00031 
<a name="l00032"></a>00032 <span class="keyword">from</span> utils.MainLog <span class="keyword">import</span> runGlobalLogger
<a name="l00033"></a>00033 <span class="keyword">from</span> utils.FemBases <span class="keyword">import</span> LagrangeP1, LagrangeP2
<a name="l00034"></a>00034 
<a name="l00035"></a>00035 <span class="keyword">import</span> models.NumericalOptionGBM <span class="keyword">as</span> nOp
<a name="l00036"></a>00036 <span class="keyword">from</span> models.AnalyticalFormulas <span class="keyword">import</span> vanillaCallPrice
<a name="l00037"></a>00037 
<a name="l00038"></a>00038 <span class="keyword">from</span> solvers.EuropeanTimeStepper <span class="keyword">import</span> EuropeanTimeStepper
<a name="l00039"></a>00039 
<a name="l00040"></a>00040 <span class="keyword">import</span> logging
<a name="l00041"></a>00041 <span class="keyword">import</span> unittest
<a name="l00042"></a>00042 
<a name="l00043"></a>00043 
<a name="l00044"></a>00044 <span class="keyword">class </span>AccurancyTestSuite(unittest.TestCase):
<a name="l00045"></a>00045 
<a name="l00046"></a>00046     <span class="keyword">def </span><a class="code" href="classtestCalibration_1_1CalibVolSurfaceCCE.html#af2080506a286e84128ed2c90232ed0e0">setUp</a>(self):
<a name="l00047"></a>00047         <span class="stringliteral">&quot;&quot;&quot; I don&#39;t know how to avoid this &quot;&quot;&quot;</span>
<a name="l00048"></a>00048 
<a name="l00049"></a>00049         self.m_r = float(0.05)
<a name="l00050"></a>00050         self.m_q = 0.0
<a name="l00051"></a>00051         self.m_sigma = float(0.2)
<a name="l00052"></a>00052         self.m_exp_time = float(1.0)
<a name="l00053"></a>00053         self.m_S0 = 40
<a name="l00054"></a>00054         self.m_K = 50
<a name="l00055"></a>00055 
<a name="l00056"></a>00056         (self.m_ntimestep_p1, self.m_nsegs_p1) = (<span class="keywordtype">None</span>, <span class="keywordtype">None</span>)
<a name="l00057"></a>00057         (self.m_ntime_step_p2, self.m_nsegs_p2) = (<span class="keywordtype">None</span>, <span class="keywordtype">None</span>)
<a name="l00058"></a>00058 
<a name="l00059"></a>00059         (self.m_Smin, self.m_Smax) = (10, 130)
<a name="l00060"></a>00060 
<a name="l00061"></a>00061         self.m_keep_hist = <span class="keyword">False</span>
<a name="l00062"></a>00062         self.m_error_tol = 0.12
<a name="l00063"></a>00063 
<a name="l00064"></a>00064         self.m_lagrangeP1 = LagrangeP1()
<a name="l00065"></a>00065         self.m_lagrangeP2 = LagrangeP2()
<a name="l00066"></a>00066 
<a name="l00067"></a>00067     <span class="keyword">def </span>_init_engine(self, option_style, scheme_type):
<a name="l00068"></a>00068         <span class="stringliteral">&quot;&quot;&quot; instantiate all the objects neede for the test case. &quot;&quot;&quot;</span>
<a name="l00069"></a>00069 
<a name="l00070"></a>00070         nsegs = {<span class="stringliteral">&#39;P1&#39;</span>: self.m_nsegs_p1,
<a name="l00071"></a>00071                  <span class="stringliteral">&#39;P2&#39;</span>: self.m_nsegs_p2}[scheme_type]
<a name="l00072"></a>00072 
<a name="l00073"></a>00073         ntime_steps = {<span class="stringliteral">&#39;P1&#39;</span>: self.m_ntimestep_p1,
<a name="l00074"></a>00074                        <span class="stringliteral">&#39;P2&#39;</span>: self.m_ntime_step_p2}[scheme_type]
<a name="l00075"></a>00075 
<a name="l00076"></a>00076         <span class="keywordflow">if</span> <span class="stringliteral">&#39;E&#39;</span> == option_style:
<a name="l00077"></a>00077             self.euOpt = nOp.NumericalOptionGBM(<span class="stringliteral">&#39;E&#39;</span>, self.m_exp_time,
<a name="l00078"></a>00078                     self.m_S0, self.m_K, ntime_steps, nsegs, self.m_Smin,
<a name="l00079"></a>00079                     self.m_Smax)
<a name="l00080"></a>00080         <span class="keywordflow">elif</span> <span class="stringliteral">&#39;A&#39;</span> == option_style:
<a name="l00081"></a>00081             self.euOpt = nOp.NumericalOptionGBM(<span class="stringliteral">&#39;A&#39;</span>, self.m_exp_time,
<a name="l00082"></a>00082                     self.m_S0, self.m_K, ntime_steps, nsegs, self.m_Smin,
<a name="l00083"></a>00083                     self.m_Smax)
<a name="l00084"></a>00084         <span class="keywordflow">else</span>:
<a name="l00085"></a>00085             <span class="keyword">assert</span> <span class="keyword">False</span>
<a name="l00086"></a>00086 
<a name="l00087"></a>00087         is_real = <span class="keyword">True</span>
<a name="l00088"></a>00088         self.euOpt.set_option_cos(self.m_sigma, self.m_q, self.m_r, is_real, \
<a name="l00089"></a>00089                 is_real, is_real)
<a name="l00090"></a>00090 
<a name="l00091"></a>00091         <span class="keywordflow">if</span> <span class="stringliteral">&#39;P1&#39;</span> == scheme_type:
<a name="l00092"></a>00092             self.euOpt.set_shape_functions(self.m_lagrangeP1)
<a name="l00093"></a>00093         <span class="keywordflow">elif</span> <span class="stringliteral">&#39;P2&#39;</span> == scheme_type:
<a name="l00094"></a>00094             self.euOpt.set_shape_functions(self.m_lagrangeP2)
<a name="l00095"></a>00095 
<a name="l00096"></a>00096 
<a name="l00097"></a><a class="code" href="classtestCompareAccurancy_1_1PlainVanillaEuroCall.html">00097</a> <span class="keyword">class </span><a class="code" href="classtestCompareAccurancy_1_1PlainVanillaEuroCall.html">PlainVanillaEuroCall</a>(AccurancyTestSuite):
<a name="l00098"></a>00098     <span class="stringliteral">&quot;&quot;&quot; under GBM model. &quot;&quot;&quot;</span>
<a name="l00099"></a>00099 
<a name="l00100"></a><a class="code" href="classtestCompareAccurancy_1_1PlainVanillaEuroCall.html#a252c92972ad883f51b588c3dc9a96645">00100</a>     <span class="keyword">def </span><a class="code" href="classtestCompareAccurancy_1_1PlainVanillaEuroCall.html#a252c92972ad883f51b588c3dc9a96645">runTest</a>(self):
<a name="l00101"></a>00101         <span class="stringliteral">&quot;&quot;&quot; overload base class. &quot;&quot;&quot;</span>
<a name="l00102"></a>00102 
<a name="l00103"></a>00103         <span class="keywordflow">print</span> <span class="stringliteral">&#39; &#39;</span>
<a name="l00104"></a>00104         self.<a class="code" href="classtestCompareAccurancy_1_1PlainVanillaEuroCall.html#a6b1ee96de013c5dda317a4a5bd0797b0">m_ntimestep_p1</a> = self.<a class="code" href="classtestCompareAccurancy_1_1PlainVanillaEuroCall.html#a4fa45acc23dc09b19832755231e03b34">m_ntime_step_p2</a> = 32
<a name="l00105"></a>00105         self.<a class="code" href="classtestCompareAccurancy_1_1PlainVanillaEuroCall.html#aef90efb8d40831e655ddedfd583cac82">m_sigma</a> = 0.31
<a name="l00106"></a>00106         rOfConvLog = logging.getLogger(<span class="stringliteral">&#39;RateOfConvergence&#39;</span>)
<a name="l00107"></a>00107         rOfConvLog.info(<span class="stringliteral">&#39;   (n time steps = &#39;</span>
<a name="l00108"></a>00108                         + str(self.<a class="code" href="classtestCompareAccurancy_1_1PlainVanillaEuroCall.html#a6b1ee96de013c5dda317a4a5bd0797b0">m_ntimestep_p1</a>) + <span class="stringliteral">&#39;)  &#39;</span> + <span class="stringliteral">&#39;(vol = &#39;</span>
<a name="l00109"></a>00109                         + str(self.<a class="code" href="classtestCompareAccurancy_1_1PlainVanillaEuroCall.html#aef90efb8d40831e655ddedfd583cac82">m_sigma</a> ** 2) + <span class="stringliteral">&#39;)  &#39;</span> + <span class="stringliteral">&#39;(r = &#39;</span>
<a name="l00110"></a>00110                         + str(self.m_r) + <span class="stringliteral">&#39;)&#39;</span>)
<a name="l00111"></a>00111         rOfConvLog.info(<span class="stringliteral">&#39;    n          error        ratio&#39;</span>)
<a name="l00112"></a>00112 
<a name="l00113"></a>00113         error_l2 = []
<a name="l00114"></a>00114         nsegs = array([int(2 ** k) <span class="keywordflow">for</span> k <span class="keywordflow">in</span> range(2, 9)], <span class="stringliteral">&#39;int&#39;</span>)
<a name="l00115"></a>00115 
<a name="l00116"></a>00116         time_stepper = <a class="code" href="classsolvers_1_1EuropeanTimeStepper_1_1EuropeanTimeStepper.html">EuropeanTimeStepper</a>()
<a name="l00117"></a>00117         time_stepper.set_number_steps(self.<a class="code" href="classtestCompareAccurancy_1_1PlainVanillaEuroCall.html#a4fa45acc23dc09b19832755231e03b34">m_ntime_step_p2</a>)
<a name="l00118"></a>00118         time_stepper.set_dolog(<span class="keyword">False</span>)
<a name="l00119"></a>00119         time_stepper.set_time2simulate(self.m_exp_time)
<a name="l00120"></a>00120         time_stepper.set_keep_hist(self.m_keep_hist)
<a name="l00121"></a>00121 
<a name="l00122"></a>00122         <span class="keywordflow">for</span> scheme_type <span class="keywordflow">in</span> [<span class="stringliteral">&#39;P1&#39;</span>, <span class="stringliteral">&#39;P2&#39;</span>]:
<a name="l00123"></a>00123             rOfConvLog.info(<span class="stringliteral">&#39;         Lagrange &#39;</span> + scheme_type)
<a name="l00124"></a>00124             prev = 0.0
<a name="l00125"></a>00125             <span class="keywordflow">for</span> k <span class="keywordflow">in</span> nsegs:
<a name="l00126"></a>00126                 self.<a class="code" href="classtestCompareAccurancy_1_1PlainVanillaEuroCall.html#adeabebbae3c3cfb3b098f765faba4ee8">m_nsegs_p1</a> = self.<a class="code" href="classtestCompareAccurancy_1_1PlainVanillaEuroCall.html#aa5cae4e10ea96c9d97c15853d888d6f7">m_nsegs_p2</a> = k
<a name="l00127"></a>00127 
<a name="l00128"></a>00128                 self._init_engine(<span class="stringliteral">&#39;E&#39;</span>, scheme_type)
<a name="l00129"></a>00129                 self.euOpt.set_dolog(<span class="keyword">False</span>)
<a name="l00130"></a>00130                 self.euOpt.set_time_stepper(time_stepper)
<a name="l00131"></a>00131 
<a name="l00132"></a>00132                 (S, CallV) = self.euOpt.price_call()
<a name="l00133"></a>00133 
<a name="l00134"></a>00134                 call_vanella_exact = vanillaCallPrice(S, self.m_K,
<a name="l00135"></a>00135                         self.m_r, self.<a class="code" href="classtestCompareAccurancy_1_1PlainVanillaEuroCall.html#aef90efb8d40831e655ddedfd583cac82">m_sigma</a>, self.m_exp_time)
<a name="l00136"></a>00136                 call_vanella_exact[call_vanella_exact &lt; 1.0e-6] = 0.0
<a name="l00137"></a>00137                 error_l2 = norm(CallV - call_vanella_exact)
<a name="l00138"></a>00138                 rOfConvLog.info(<span class="stringliteral">&#39; %5d    %12.11f    %12.11f&#39;</span> % (k,
<a name="l00139"></a>00139                                 error_l2, prev / error_l2))
<a name="l00140"></a>00140                 prev = error_l2
<a name="l00141"></a>00141             rOfConvLog.info(<span class="stringliteral">&#39;&#39;</span>)
<a name="l00142"></a>00142 
<a name="l00143"></a>00143 
<a name="l00144"></a>00144 <span class="keyword">def </span>mySuite():
<a name="l00145"></a>00145     <span class="stringliteral">&quot;&quot;&quot; all test cases in the suite. &quot;&quot;&quot;</span>
<a name="l00146"></a>00146 
<a name="l00147"></a>00147     suite = unittest.TestSuite()
<a name="l00148"></a>00148     suite.addTest(<a class="code" href="classtestCompareAccurancy_1_1PlainVanillaEuroCall.html">PlainVanillaEuroCall</a>())
<a name="l00149"></a>00149     <span class="keywordflow">return</span> suite
<a name="l00150"></a>00150 
<a name="l00151"></a>00151 
<a name="l00152"></a>00152 <span class="keywordflow">if</span> __name__ == <span class="stringliteral">&#39;__main__&#39;</span>:
<a name="l00153"></a>00153 
<a name="l00154"></a>00154     runGlobalLogger()
<a name="l00155"></a>00155     runner = unittest.TextTestRunner(verbosity=2)
<a name="l00156"></a>00156     result = runner.run(mySuite())
<a name="l00157"></a>00157 
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